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Simplifying 12x + 4x2 = 98 Solving 12x + 4x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + 12x + 4x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + 6x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying -49 + 6x + 2x2 = 0 Solving -49 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24.5 + 3x + x2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + 3x + 24.5 + x2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + 3x + x2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + 3x + x2 = 0 + 24.5 3x + x2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 3x + x2 = 24.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 24.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 24.5 + 2.25 Combine like terms: 24.5 + 2.25 = 26.75 2.25 + 3x + x2 = 26.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 26.75 Calculate the square root of the right side: 5.172040216 Break this problem into two subproblems by setting (x + 1.5) equal to 5.172040216 and -5.172040216.Subproblem 1
x + 1.5 = 5.172040216 Simplifying x + 1.5 = 5.172040216 Reorder the terms: 1.5 + x = 5.172040216 Solving 1.5 + x = 5.172040216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5.172040216 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.172040216 + -1.5 x = 5.172040216 + -1.5 Combine like terms: 5.172040216 + -1.5 = 3.672040216 x = 3.672040216 Simplifying x = 3.672040216Subproblem 2
x + 1.5 = -5.172040216 Simplifying x + 1.5 = -5.172040216 Reorder the terms: 1.5 + x = -5.172040216 Solving 1.5 + x = -5.172040216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5.172040216 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.172040216 + -1.5 x = -5.172040216 + -1.5 Combine like terms: -5.172040216 + -1.5 = -6.672040216 x = -6.672040216 Simplifying x = -6.672040216Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.672040216, -6.672040216}Solution
x = {3.672040216, -6.672040216}
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